The logic called ATL (Alternating-time Temporal Logic) was introduced, in 1997, as a modal logic of agents. The first direct algorithm to test whether a given ATL-formula θ is satisfiable was provided by V. Goranko and G. van Drimmelen in 2006. Their algorithm is based on alternating infinite tree automata. In 2009, V. Goranko and D. Shkatov proposed a method to test satisfiability of a formula...

We give a general approach to show the closure under complement and decide the emptiness for many classes of multistack visibly pushdown automata (Mvpa). A central notion in our approach is the visibly path-tree, i.e., a stack tree with the encoding of a path that denotes a linear ordering of the nodes. We show that the set of all such trees with a bounded size labeling is regular, and path-tre...

A data tree is a tree whose every node carries a label from a finite alphabet and a datum from some infinite domain. We introduce a new model of automata over unranked data trees with a decidable emptiness problem. It is essentially a bottom-up alternating automaton with one register, enriched with epsilon-transitions that perform tests on the data values of the subtree. We show that it capture...

In this paper we present Regular XPath (RXPath), which is a natural extension of XPath with regular expressions over paths that has the same computational properties as XPath: linear-time query evaluation and exponential-time reasoning. To establish these results, we devise a unifying automata-theoretic framework based on two-way weak alternating tree automata. Specifically, we consider automat...

We develop an automata-theoretic framework for reasoning about linear properties of infinite-state sequential systems. Our framework is based on the observation that states of such systems, which carry a finite but unbounded amount of information, can be viewed as nodes in an infinite tree, and transitions between states can be simulated by finite-state automata. Checking that the system satisf...

In this paper, at first we define the concepts of response function and accessible states of a complete residuated lattice-valued (for simplicity we write $mathcal{L}$-valued) tree automaton with a threshold $c.$ Then, related to these concepts, we prove some lemmas and theorems that are applied in considering some decision problems such as finiteness-value and emptiness-value of recognizable t...

We propose a fibred monoidal closed category of alternating tree automata, based on a Dialectica-like approach to the fibred game model of [17]. Alternating tree automata are equivalent in expressive power to the Monadic Second-Order Logic on infinite trees (MSO), which subsumes most of the logics used in verification (see e.g. [14, 5]). Acceptance of an input tree t by an automaton A can be de...

For deterministic tree automata, classical hierarchies, like MostowskiRabin (or index) hierarchy, Borel hierarchy, or Wadge hierarchy, are known to be decidable. However, when it comes to non-deterministic tree automata, none of these hierarchies is even close to be understood. Here we make an attempt in paving the way towards a clear understanding of tree automata. We concentrate on the class ...